This paper establishes that the local k-Ramsey number R(K m , k -loc) is identical with the mean k-Ramsey number R(K m , k -mean). This answers part of a question raised by Caro and Tuza.
More rotation numbers for complete bipartite graphs
✍ Scribed by Béla Bollobás; E. J. Cockayne
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 285 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let G be a simple undirected graph which has p vertices and is rooted at x. Informally, the rotation number h(G, x) of this rooted graph is the minimum number of edges in a p vertex graph H such that for each vertex v of H, there exists a copy of G in H with the root x at v. In this article we calculate some rotation numbers for complete bipartite graphs, and thus greatly extend earlier results of Cockayne and Lorimer.
📜 SIMILAR VOLUMES
The Ramsey numbers M,,, n,P,, ..., n,P,), p > 2, are calculated. ## 1. Introduction One class of generalized Ramsey numbers that are known exactly are those for the graphs nP2 which consist of n disjoint paths of length 2; E. J. Cockayne and the author proved in 111 that d r(nlp2, ..., n d P 2 ) =
## Abstract Given a graph __G__ and an integer __k__ ≥ 1, let α(__G, k__) denote the number of __k__‐independent partitions of __G__. Let 𝒦^−s^(__p,q__) (resp., 𝒦~2~^−s^(__p,q__)) denote the family of connected (resp., 2‐connected) graphs which are obtained from the complete bipartite graph __K~p,q